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Magnetostrictive actuators exhibit inherent asymmetric hysteresis nonlinearities. In this paper, an asymmetric shifted Prandtl-Ishlinskii (ASPI) model was first proposed, being composed by three components: a Prandtl-Ishlinskii (PI) operator, a shift operator and a Lipschitz-continuous function. The benefits for such a model are that it can represent the asymmetric hysteresis behavior and facilities construction of the analytic inverse model for the purpose of mitigating the hysteresis effects of the magnetostrictive actuator. Experimental tests were then conducted on the magnetostrictive actuator. The experimental results validated the modeling accuracy of the ASPI model and the effectiveness of the proposed inverse compensation method.